Study of optimal order policy for a multi-period multi-raw material inventory management problem under carbon emission constraint

Abstract

In recent years, the carbon emission problem involved in various industries has attracted more and more attention from scholars, among which many scholars have incorporated the carbon emission problem into the inventory control process of the manufacturing industry. Motivated by this fact, assuming carbon cost is only incurred during the transportation, we develop a multi-period, multi-item periodic-review dynamic programming model to address the raw-material inventory management problem in a foundry enterprise. This model enables us to further compare two production strategies (strategy α and strategy β). The former represents the strategy to scale down the original consumption rate of raw materials in an equal proportion on the premise of maximizing meeting the carbon emission limit, and the latter represents the strategy to keep the original raw material consumption rate constant in early stage, but are taken to stop production when the carbon emissions are saturated. Due to the complexity of the proposed problem, we propose a mathematic algorithm based on Probabilistic Dynamic Programming (PDP) to derive the structural properties of the model. Groups of comparison of the expected total cost under different strategies lead to the observation that production strategy α generally performs better than production strategy β. Intriguingly, the sum of the initial inventory level and the optimal order quantity is approximately constant in one period. This phenomenon lasts for different periods under the same production strategy.